An RDF example using the Apex RDF plugin

Apex a43 includes a new RDF generation plugin. Here’s an example of some data taken with the plugin. Thanks to Dieter Isheim of Northwestern University for a sample dataset. In this case, it is the Fe alloy with Ni, Cu and Al, and a number of other components. In the picture below, Cu atoms are in red, and visually they appear in clusters.

First, I use ‘Select Points’ mode to make a simple selection in the dataset. Thats the rectangular area shown where the atoms are drawn slightly darker. This selected range includes about 118,000 atoms, 2093 of which are Cu atoms. These 2093 atoms will be used as the reference points in the RDF calculation.

From Clipboard.gif

I choose the ‘RDF Export’ menu item and select the parameters I want — Cu atoms for reference, 1600 bins and cutoff radius of 40 Ångstroms. I specify the name for the output file, in this case ‘Cu44 3.rdf’. The calculation takes 40 seconds. In that time, Apex has gone through each of the 2093 Cu atoms, found all of the other atoms in the dataset in a 40 Ångstrom radius, and measured the distance to each reference atom and binned all the results, writing out a tab-delimited file. I go to my graphing application proFit , and choose ‘Import’. Here I can specify that the file contains its own column headers,and this is the window that gets created:

RDFChartData.gif

In short order, I’ve got a graph that looks like this:

RDFGraph.gif

A few things to note. The red line is the most interesting. What it means is that the density of Cu is a lot higher near your average Cu atom than further away: That’s the same thing as seeing the Cu atoms in clusters in the atom map, but in the RDF, you can see how big the clusters are. The plot drops down significantly between 5 and 10 Ångstroms, which is indicative of clusters of about 20 Ångstroms in size. This kind of data is fun to interpret, because it is an average over all the reference atoms, some of which are in the center of a cluster, some of which are near the edge of a cluster, and the clusters aren’t necessarily spherical or uniform in size.

Second thing to note is that the Ni and Al also have slightly higher concentrations near Cu than farther away, but that the Aluminum concentration drops off faster than the Ni — out at a radius of 20 Å, the Ni concentration is double that of the Al. So there is a much stronger correlation of the Al with the Cu than of Ni with Cu.

the Fe concentration stays pretty flat despite a higher density of the other components near Cu atoms. Does this mean that there is actually a higher atomic density in the sample near the Cu clusters? Well, no. There are any number of Atom Probe conditions which might cause this sort of data anomaly: one possibility is that the radius of the tip may change as a function of chemical composition of the tip — and thus the magnification changes, too, producing changes in the apparent density. This effect is quite common. The efficiency of detection may also change as a function of composition — the Atom Probe may only collect 50% of the atoms in any given sample — other are lost due to bad ion optics, or evaporation outside of the pulse window, or multiple atom evaporation, or other electrical noise. Another effect is that some of the reference atoms may be close to edges in the dataset itself, which means that those reference atoms are not surrounded by a 40 Å radius of atoms, which would result in a decrease of the total density with increasing radius.

A common ploy to correct all these effects is to make a plot of concentration, rather than density (Dieter says he prefers that, actually). It is easy to do that in this case, as the total number of atoms is already supplied in the dataset in column 2.

Some RDF datasets also show short range order: that is, down in the 2 -3 Ångstrom range, it is possible to see the effects of first-nearest neighbor positions vs, second or third nearest neighbor positions. This dataset doesn’t show any such interesting pattern.

Lastly, one feature of the RDF that we calculate is the gradually changing binsize. As noted here previously, data analysis in the Atom Probe is often a tradeoff of positional error vs. statistical sampling error. Because the number of atoms at a given radius increases with r squared, we expect to have less error in the measurement at higher radii. In our calculation, we show both lower sampling error and lower statistical sampling error as the radius increases, by decreasing the binsize with increasing radius. This is reflected in the data: At lower radii, the scatter in the data is higher, and there is slightly more distance between the datapoints.

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